Check the picture below, so the parabola looks more or less like so.
keeping in mind the vertex is half-way between the focus point and the directrix, this one lands as you see it in the picture, with a negative "p" distance.
[tex]\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{"p"~is~negative}{op ens~\cap}\qquad \stackrel{"p"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=-5\\ k=0\\ p=-2 \end{cases}\implies 4(-2)(y-0)=( ~~ x-(-5) ~~ )^2\implies -8y=(x+5)^2 \\\\\\ ~\hfill {\Large \begin{array}{llll} y=-\cfrac{1}{8}(x+5)^2 \end{array}} ~\hfill[/tex]
Math Test!!
1. Austin bought 5 pizza's for the football team, each play is going to eat 2/3 of a pizza. what is the greatest number of players that he can feed?
A. 6
B. 7
C. 8
D. 9
2. Carolyn is practicing for her upcoming triathlon she is going to run 4 miles how many quarter miles is this?
A. 4
B. 12
C. 16
D. 20
3. for the last 3 hours, Shantell has been writing a research paper she writes a page every 2/3 hour how many pages has she written?
A. 4 1/2
B. 4 1/3
C. 4 1/4
D. 4/ 2/3
4. Wallace has a board 4 feet long he is cutting off pieces that are 3/4 of a foot long. How many pieces can he make?
A. 4
B. 5
C. 6
D. 7
5. Demetria has been downloading songs for 8 minutes if each song takes 2/5 of a minute to download, how many songs has she downloaded?
A. 14
B. 16
C. 18
D. 20
30. Write in standard form
1.15 x 10 to the power of negative 5
31. Write in standard form
2.2 x 10 to the power of negative 10
32. Write in standard form
4.3 x 10 to the power of 10
Answer:
30) 0.0,000,115
31) 0.00,000,000,022
32) 43,000,000,000
Step-by-step explanation:
30
1.15 x [tex]10^{-5}[/tex] The negative exponent is telling us that the number in standards form is smaller than 1.15. To write in standard form we move the decimal 5 places to the left.
0.0,000,115
31
2.2 x [tex]10^{-10}[/tex] This is like question 30, but we will move the decimal 10 places to the left this time.
0.00,000,000,022
32
4.3 x [tex]10^{10}[/tex] the exponent is positive this time. That means in standard from the number is much larger than 4.3. Move the decimal point 10 places to the right. If you do not see a decimal point, it means that it is at the end of the number.
43,000,000,000
Please help me. I know it’s 4 months but I don’t know what the total amount paid is including interest. If anyone could add the steps that would be awesome!
Divide by 12 to go from the APR to the monthly interest rate
(9.5%)/12 = 0.7916667%
The decimal form is 0.007916667 approximately.
Multiply this with the starting balance $1367.90 and we get:
0.007916667*1367.90 = 10.8292 which rounds to 10.83
The interest payment for the 1st month is $10.83; which means the principal payment would be 400-10.83 = 389.17
This principal payment will then drop the balance from $1367.90 to 1367.90-389.17 = 978.73 dollars.
The value $978.73 is now the starting balance of the 2nd month. This process of...
(a) Compute the interest(b) Subtract the interest from the $400 monthly payment to get the principal (with the exception of the last month as shown below)(c) Subtract the principal from the starting balance to get the ending balance.is repeated until the balance is $0.
This is what the table would look like
[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6}\text{Month} & \text{Starting} & \text{Interest} & \text{Principal} & \text{Payment} & \text{Ending }\\& \text{Balance} & & & & \text{Balance}\\\cline{1-6}1 & 1367.9 & 10.83 & 389.17 & 400 & 978.73\\\cline{1-6}2 & 978.73 & 7.75 & 392.25 & 400 & 586.48\\\cline{1-6}3 & 586.48 & 4.64 & 395.36 & 400 & 191.12\\\cline{1-6}4 & 191.12 & 1.51 & 191.12 & 192.63 & 0\\\cline{1-6}\end{array}[/tex]
Many credit card companies and banks offer free calculators on their website, or you can find similar free calculators online elsewhere, that will quickly calculate a table like shown above. It is called an amortization table or amortization schedule.
With the exception of the 4th month, each row has the principal and interest add to the $400 monthly payment. The last row will have a payment of 1.51+191.12 = 192.63 dollars.
The total amount paid back would be 400+400+400+192.63 = 1392.63 dollars. This is the sum of the values in the "payment" column.
-------------------------------------------------------------------------
Here's another way to determine the answer.
The monthly payment formula is
[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}[/tex]
where,
P = monthly paymentL = loan amount, aka starting balancei = monthly interest rate in decimal formn = number of monthsIn this case,
P = 400L = 1367.90i = 0.007916667 approximately (calculated earlier)n = unknownLet's solve for the variable n. We'll need logarithms to isolate the exponent.
Part 1
[tex]\displaystyle P = \frac{Li}{1 - (1+i)^{-n}}\\\\\\\displaystyle 400 = \frac{1367.90*0.007916667}{1 - (1+0.007916667)^{-n}}\\\\\\\displaystyle 400 = \frac{10.8292087893}{1 - (1.007916667)^{-n}}\\\\\\\displaystyle 400(1 - (1.007916667)^{-n}) = 10.8292087893\\\\\\[/tex]
Part 2
[tex]\displaystyle 1 - (1.007916667)^{-n} = 10.8292087893/400\\\\\\\displaystyle 1 - (1.007916667)^{-n} = 0.0270730\\\\\\\displaystyle -(1.007916667)^{-n} = 0.0270730-1\\\\\\\displaystyle -(1.007916667)^{-n} = -0.9729270\\\\\\\displaystyle (1.007916667)^{-n} = 0.9729270\\\\\\[/tex]
Part 3
[tex]\displaystyle \log((1.007916667)^{-n}) = \log(0.9729270)\\\\\\\displaystyle -n*\log(1.007916667) = \log(0.9729270)\\\\\\\displaystyle n = -\log(0.9729270)/\log(1.007916667)\\\\\\\displaystyle n = 3.4805965\\\\\\[/tex]
Each decimal value is approximate.
That value of n then rounds up to the nearest integer n = 4
We do not round to n = 3 since that would be one month short, as shown in the table above.
You can use a graphing calculator to quickly solve that equation for the variable n. It can be used as a way to visually confirm the answer.
Dustin has $1,000 in a savings account that earns 10% interest per year. The interest is not compounded. How much will he have in total in 1 year? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
1,100
Step-by-step explanation:
1000 x 0.1 = 100
1000 + 100 = 1,100
The hypothetical city of hurstville is trying to decide how many city beautification projects should be approved each year. These projects involve planting gardens, commissioning murals, and building fountains. The city has two types of citizens. Type b citizens appreciate beauty more than type a citizens. There is an equal number of each type of citizen. The accompanying schedule depicts each type of citizen's marginal benefit for city beautification projects. The average cost of each project is $400. Use the information in the schedule to answer the questions. Marginal benefit scheduleqmbambb04006001300500220040031003004020050100600what is the optimal quantity of city beautification projects?3124city beautification is a public good because:it is nonrival in consumption and nonexcludable. It is rival in consumption and excludable. It is rival in consumption and nonexcludable. It is nonrival in consumption and excludable
Using the provided information we get,
a) Optimal quantity of city beautification projects is three.
b) 3124 city beautification is a public good because it is rival in consumption and non-excludable. So, Correct option is option (C).
The fictional city of Hurstville is trying to determine how many urban beautification projects it has. The city has two types of citizens, ones who appreciates beauty more than other type.
The average cost of each project = $400
We have given that
The combined marginal benefit curves are determined by horizontally adding up the in the individual marginal benefit curves. So, the optimal quantity of benefication projects is at the point where MSB is equal to MSE. Thus, the optimal outputs is 3 projects.
The city beneficiation is a public good because it is non-trivial in consumption and non-excludable.
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helpp
i need it rnn
and if u could plot the point too thats good
js those for now tyy
Step-by-step explanation:
5.
y = 3
yes, that's it for this here too.
it means that any value for x is valid, and all have the assigned y value 3.
6.
remember, the usual equation for a line is
y = ax + b
"a" being the slope, "b" the y-intercept (the y-value when x = 0).
we see the y-value for x = 0 is 3. that is "b".
for the slope we need 2 points and calculate the x- and y- coordinate differences.
always look for points with integer coordinates.
I see e.g. (0, 3) and (3, 2).
x changes by +3 (from 0 to 3).
y charges by -1 (from 3 to 2).
the slope "a" = -1/+3 = -1/3
the equation is then
y = (-1/3)x + 3
7.
we do exactly the same things.
we see the y-value for x = 0 is +1. that is "b".
I see e.g. these points : (0, 1) and (3, 2).
x changes by +3 (from 0 to 3).
y changes by +1 (from 1 to 2).
the slope "a" is +1/+3 = 1/3.
the equation is
y = (1/3)x + 1
8.
and again the same things.
we see the y-value for x = 0 is +3. that is "b".
I see e.g. these points : (0, 3) and (-3, 0).
x changes by -3 (from 0 to -3).
y changes by -3 (from 3 to 0).
the slope "a" is -3/-3 = 3/3 = 1.
the equation is
y = x + 3
Given the equation a line y+9=-3(x-4) Determine the characteristics of the line.
Answer:
Step-by-step explanation: y+9=-3(x-4)......given equation
This equation can be expanded further and simplified
y+9=-3x+12
We want to put the equation into the form y=mx+b so we can read its characteristics
To do this we need to get y on its own. We must take 9 from both sides
y+9-9=-3x-9+12
y=-3x+3
The equation has a gradient or slope or m =-3 and it cuts the y-axis at +3 or is the yintercept
What is the inverse function for -2f(x+5)-4
Answer:
Read carefully below
Step-by-step explanation:
In general, the inverse of a function f(x) is a function g(x) such that f(g(x)) = g(f(x)) = x for all values of x in the domain of f(x) and g(x). To find the inverse of a function, we need to switch the input and output variables and solve for the new output variable.
In this case, we are given the function -2f(x+5)-4. To find the inverse of this function, we need to switch the input and output variables and solve for the new output variable, which we will call y. We can do this by first moving all the terms to one side of the equation, and then solving for y:
-2f(x+5) - 4 = y
-2f(x+5) = y + 4
f(x+5) = (y + 4) / -2
This is the inverse function of -2f(x+5)-4. However, keep in mind that not all functions have inverses. In particular, a function must have the property that it is one-to-one (i.e. it maps unique inputs to unique outputs) in order to have an inverse. It is not clear from the given information whether the function -2f(x+5)-4 is one-to-one, so it is possible that it does not have an inverse.
find a function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
A function f such that f '(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f is f(x) = 3x^4/4 + 729/4.
In the given question, we have to find a function f such that f'(x) = 3x^3 and the line 81x + y = 0 is tangent to the graph of f.
The given function is f'(x) = 3x^3.
No integrating on both side,
f(x) = [tex]\int3x^3dx[/tex] + C
f(x) = 3x^4/4 + C
As given, the line 81x + y = 0 is tangent to the graph of f.
So, slope at point of tangent; f'(x) = -81
So, 3x^3 = -81
Divide by 3 on both side, we get
x^3 = -27
Taking cube root on both side, we get
x = -3
So putting the value of x in 81x + y = 0, we get
y = 243
Thus, f(x) passes through (-3, 243).
So, 243 = 3/4(81) + C
Multiply by 4 on both side, we get
972 = 243 + 4C
Subtract 243 on both side, we get
4C = 729
Divide by 4 on both side, we get
C = 729/4
So, f(x) = 3x^4/4 + 729/4
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Complete this working to write 9³ as a power of 3
9³=9x9
SO
SO
9³3 x 3 x 3 x
=
9³ = 3
where y =
Answer:
y= 6
Step-by-step explanation:
9³ = 3^y
3²^³ = 3^y
3⁶ = 3^y
therefore
y=6
You're at a clothing store that dyes your clothes while you wait. You get to pick from 4 44 pieces of clothing (shirt, pants, socks, or hat) and 3 33 colors (purple, blue, or orange). If you randomly pick the piece of clothing and the color, what is the probability that you'll end up with an orange hat?.
The probability of ending up with an orange hat is 1/12. It is because here are twelve possible outcomes.
What is Probability?Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.
It is represented mathematically as;
Probability = Number of Expected outcomes / Total number of outcomes
From the question, we can have the following outcomes;
Clothing = 4
Colors = 3
Pr (pick a clothing) = 1/4
Pr (pick a color) = 1/3
Pr (picking an orange hat) = 1/4 x 1/3
Pr (picking an orange hat) = 1/12.
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A worker bee has a mass of 2 x 10^-4 kilograms. There are
8 x 10^4worker bees living in one hive. What is the mass
of all the worker bees in the hive together?
•Write your final answer in STANDARD form.
•Only type in the numerical answer.
To find the total mass of all the worker bees in the hive, you need to multiply the mass of a single worker bee by the number of worker bees in the hive.
The mass of a single worker bee is 2 x 10^-4 kilograms, and there are 8 x 10^4 worker bees in the hive.
So the total mass of all the worker bees in the hive is (2 x 10^-4 kilograms) * (8 x 10^4 worker bees) = 0.16 kilograms.
In standard form, this is written as 1.6 x 10^-1 kilograms.
Suppose that an individual has a body fat percentage of 15.7% and weighs 162 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.
If m<5 = (8x-14) and m<7 = (5x+34), what is the value of x and m<5?
Answer:
maybe 16
I hope I helped
Step-by-step explanation:
joining m < 5 = m < 7
8x – 14 = 5x + 34
8x – 5x = 34 + 14
3x = 48
divide both sides by 3
x = 48/3
x = 16
Which is closest to the volume of the cylinder below?
A. 6.28 cubic cm
B. 12.56 cubic cm
C. 62.8 cubic cm
D. 125.6 cubic cm
The illustrated volume of the cylinder is 769cm³.
How to calculate the volume?One of the most fundamental curvilinear geometric shapes, a cylinder has traditionally been a three-dimensional solid. It is regarded as a prism with a circle as its base in basic geometry. In many contemporary branches of geometry and topology, a cylinder can also be defined as an infinite curvilinear surface.
It should be noted that the formula for finding the volume of a cylinder is πr²h
where π = 3.14
r = radius
h = height
Let's assume that the height is 5cm and radius is 7cm. The volume will be:
V = πr²h
Volume = 3.14 × 7² × 5
Volume = 769cm³
Note that your information was incomplete and an overview was given.
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Nakida read that the number of time a cricket chirp depend on the temperature of the air. The cientit found that the number of chirp per minute i equal to 0. 23 time the temperature of the air, in degree Fahrenheit, plu forty. X y a. Write an equation that repreent the number of time a cricket chirp given the temperature in degree Fahrenheit
The equation that represents the number of time a cricket chirp (y) given the temperature (x) in degree Fahrenheit is y = 0.23 x + 40
Steps to translate a word problem into an equation or a function:
- Assign the unknowns to variables
- Identify which one is independent variables, which one is dependent variables. The independent variable will become the input while the dependent variable will become the output.
In the given problem, there are two variables:
- temperature in the air (in Fahrenheit)
- number of time a cricket chirp
From the problem, we can conclude that the number of time a cricket chirp depends on the temperature of the air. Hence,
independent variable = temperature in the air (in Fahrenheit)
dependent variable = number of time a cricket chirp
Let:
y = number of time a cricket chirp
x = temperature in the air (in Fahrenheit)
It is said: The number of chirp per minute is equal to 0. 23 times the temperature of the air, in degree Fahrenheit, plus forty.
We can translate it into an equation:
y = 0.23 x + 40
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Your car holds at most 14.5 gallons of gas. on the way to the grocery store, you use 1.5 gallons of gas. write an inequality to show the amount of gas you have left in your tank.
Answer:
Step-by-step explanation:
If the car holds at most 14.5 gallons of gas and you use 1.5 gallons of gas on the way to the grocery store, the amount of gas you have left in your tank can be represented by the inequality:
[tex]14.5 - 1.5 < = x[/tex]
This inequality can be read as "14.5 minus 1.5 is less than or equal to the amount of gas you have left in your tank, x."
Solving for x, we get:
[tex]x > = 13[/tex]
So the amount of gas you have left in your tank is greater than or equal to 13 gallons.
What is the prime factorization of 168?
22 x 32 x 5
34 x 7
22 x 17
23 x 3 x 7
Answer:
2,3 and 7
Step-by-step explanation:
168 = 2x2x2x3x7
= 2²x3x7
Which expression is equivalent to 2 and three tenths raised to the fourth power divided by nine tenths raised to the fifth power, all raised to the fourth power?
2 and three tenths raised to the eighth power divided by nine tenths raised to the ninth power
2 and three tenths raised to the sixteenth power divided by nine tenths raised to the twentieth power
1.44
1.49
The equivalent expression to {(2 3/10)⁴ ÷ (9/10)⁵}⁴ is "2 and three tenths raised to the sixteenth power divided by nine tenths raised to the twentieth power".
The correct answer choice is option B
Which is the equivalent expression?Exponents refers to the power to which a number, expression or symbol is to be raised. For instance, 4²; the exponent is 2 which is a power.
{(2 3/10)⁴ ÷ (9/10)⁵}⁴
= (2.3⁴ ÷ 0.9⁵)⁴
Multiply the powers
= 2.3¹⁶ ÷ 0.9²⁰
It can also be written as
(2.3)¹⁶ / (0.9)²⁰
Consequently, the expression which is equivalent to 2 and three tenths raised to the fourth power divided by nine tenths raised to the fifth power, all raised to the fourth power is (2.3)¹⁶ / (0.9)²⁰
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Answer:
I am 100% sure it is b
Step-by-step explanation:
I have proof( i did the test) and took a picture
What is the answer to 19(2m−16)=13(2m+4)
Answer:
m = -21.
Step-by-step explanation:
To solve this equation, we can use the distributive property to expand the left side and the right side of the equation:
19(2m - 16) = 13(2m + 4)
38m - 304 = 26m + 52
Then we can combine like terms on both sides of the equation to obtain:
38m - 26m = 52 - 304
12m = -252
Finally, we can divide both sides of the equation by 12 to find the value of m:
12m / 12 = -252 / 12
m = -21
Therefore, the value of m that satisfies the equation is m = -21.
Please hellp this is do today I will give brainlyest
Answer:
Step-by-step explanation:
Answer is B.
Function 1: slope is 2
Function 2: (-5 + 4)/(2-1)= -1/1= -1
A Venu revolve around the un, it travel at a peed of approximately 22 mile per econd. Convert thi peed to mile per minute. At thi peed, how many mile will Venu travel in 6 minute?
Answer:
22mile=1sec
x=360sec
criss cross method
(x)(1)=360×22
x=7920miles
the unicode character set is a subset of the ascii character set. group of answer choices true false
It s true that a text file contains bytes of data that represent characters from a particular character set such as Unicode or ASCII. The correct option to this question is "True".
The text file contains texts that are represented by Unicode or ASCII. The Unicode or ASCII represents how the numbers, text, or other commands are displayed and written in a text file.
To represent text digitally in the text file, characters have their own unique character representation bit-pattern. These bit-pattern have a combination of 1s and 0s. And these patterns are represented by character codes that are either Unicode or ASCII.
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at what point is the tangent to f(x)=x^2+4x-1 horizontal
The point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].
To find the tangent of a curve, we have to find the first derivative of the function. Hence, the tangent of the given curve is given by
⇒ [tex]f'(x) = \frac{d{f(x)}}{dx} = \frac{d{x^{2}}}{dx} + \frac{d(4x)}{dx} - \frac{d(1)}{dx}[/tex]
⇒ [tex]f'(x) = 2x + 4[/tex]
Now, as the tangent is horizontal, that means the slope of the tangent is 0, hence setting [tex]f'(x) = 0[/tex] , we get the equation
⇒ [tex]f'(x) = 2x + 4 = 0[/tex]
Solving the equation obtained for the variable x,
⇒ [tex]2x = -4\\[/tex]
⇒ [tex]x = -2[/tex]
Now, putting the obtained value for x in the original equation, we get
⇒ [tex]f(x) = (-2)^{2} + 4(-2) - 1\\[/tex]
⇒ [tex]f(x) = -5[/tex]
Hence, the point where the tangent to the given equation is horizontal is [tex](x, y) = (-2, -5)[/tex].
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find the sum of 2 over 3 + negative 1 over 3
Answer:
2/3 + -1/3 = positive 1/3
Answer:
To find the sum of 2/3 + (-1)/3, you can first convert the fraction to an equivalent fraction with a common denominator. In this case, the common denominator would be 3. 2/3 can be written as 2 x (3/3) = 2/3 and -1/3 can be written as -1 x (3/3) = -1/3. Then, you can add the numerators and the denominator will remain the same. So, the sum of 2/3 + (-1)/3 is 1/3.
At a hockey game, a vender sold a combined total of 250 sodas and hot dogs. The number of sodas sold was 42 more than the number of hot dogs sold. Find the number of sodas sold and the number of hot dogs sold.
sodas sold:
hotdogs sold:
Answer:
let x as hotdog and x + 42 as soda
x + x + 42 = 250
2x + 42 = 250
2x + 42 - 42 = 250 - 42
2x = 208
x = 104
sodas sold: x + 42 = 104 + 42 = 146 sodas
hotdogs sold: x = 104 hotdogs
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-Answer:
104 hot dogs sold
146 sodas sold
Step-by-step explanation:
s=number of sodas. h=number of hotdogs
s+h=250
s=h+42 ==> there were 42 more sells for soda than compared to hot dog
h+42+h=250 ==> plugin h+42 for s
h+h+42=250 ==> simplify
2h+42=250 ==> solve for h
2h+42-42=250-42 ==> isolate h by subtracting 42 on both sides
2h = 208
h = 208/2
h = 104 hot dogs sold
s=104+42 ==> plug in 104 for h in s=h+42
s = 146 sodas sold
AXYZ is similar to ALMN. Angle Y is 89
degrees and Angle N is 32 degrees.
Record the measures for each angle in
the diagram.
The measurement of angles △XYZ are ∠X = 59°, ∠Y = 89°, and ∠Z = 32°.
The measurement of angles △LMN are ∠L = 59°, ∠M = 89°, and ∠N = 32°.
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
Given that, △XYZ and △LMN are similar triangle.
Since the triangles are similar, thus the measurement of triangles are similar.
Therefore,
∠X = ∠L, ∠Y = ∠M, ∠Z = ∠N.
∠Y = ∠M = 89° and ∠Z = ∠N = 32°.
The sum of all interior angles of triangle is 180°.
∠X + ∠Y + ∠Z = 180°
∠X + 89° + 32° = 180°
∠X + 121° = 180°
Subtract 121° from both sides:
∠X = 59°
∠X = ∠L = 59°.
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In the right △ABC with m∠C=90°, m∠B=75°, and AB=12 cm. Find the area of △ABC.
Please try to solve with without sin, cos, or any square roots.
Also, please do ASAP
ill award Brainliest if solved correctly without sin, cos, or any square roots!
Answer:
To find the area of a triangle, we can use the formula:
Area = (base * height) / 2
To find the area of triangle ABC, we first need to find the base and the height.
Since angle B is 75 degrees, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle A: 180 - 75 - 90 = 15 degrees.
Then, we can use the fact that the measure of an angle in a triangle is proportional to the length of the side opposite that angle to find the length of side AC:
AC/AB = m∠A/m∠B
AC = (m∠A/m∠B) * AB
Substituting, we get:
AC = (15/75) * 12 = 3
Now that we know the base and the height of the triangle, we can use the formula to find the area:
Area = (3 * 12) / 2 = 18
Therefore, the area of triangle ABC is 18 square cm.
find the work in ft-lb done by winding up a hanging cable of length 100 ft and weight-density 5 lb/ft
the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.
A force applied across a distance is what is referred to as work.
In this problem,
the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft).
Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done.Work is a force applied across a distance, and it is measured in a unit of energy called foot-pounds. In this problem, the force applied is the weight of the cable (5 lb/ft) multiplied by the length of the cable (100 ft). Therefore, the work done is equal to the force applied (500 lb) multiplied by the distance (100 ft), resulting in 500 ft-lb of work done. This means that 500 ft-lb of energy must be expended in order to move the cable 100 ft. This energy can be provided by a variety of sources, such as human labor, a motor, or some other mechanism.
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Sofia ordered sushi for a company meeting. They change plans and increase how many people
will be at the meeting, so they need at least 100 pieces of sushi in total.
and paid for 24 pieces of sushi, so she needs to
Sofia had already ordered
order additional sushi.
The sushi comes in rolls, and each roll contains 12 pieces and costs $8.
Answer: Sofia needs to order an additional 100 - 24 = 76 pieces of sushi.
Since each roll contains 12 pieces, Sofia needs to order 76 / 12 = 6 additional rolls of sushi.
At a cost of $8 per roll, Sofia will need to pay an additional 6 * $8 = $48 for the additional sushi.
Step-by-step explanation: